url stringclasses 147
values | commit stringclasses 147
values | file_path stringlengths 7 101 | full_name stringlengths 1 94 | start stringlengths 6 10 | end stringlengths 6 11 | tactic stringlengths 1 11.2k | state_before stringlengths 3 2.09M | state_after stringlengths 6 2.09M | input stringlengths 73 2.09M |
|---|---|---|---|---|---|---|---|---|---|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | apply congr.coinduction r' | case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
i : I
x y : IContainer.M (C F) i... | case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
i : I
x y : IContainer.M (C F)... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i =>... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | . clear hβ
intro i x y hβ
simp only [precongr, map_quot]
have hβ := hβ i _ _ hβ
simp only [destruct, destruct.f] at hβ
generalize IContainer.M.destruct x = x at *
generalize IContainer.M.destruct y = y at *
cases x with | mk nx kx =>
cases y with | mk ny ky =>
let f i : Quot (r i) β Quot (r' i) :=
... | case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
i : I
x y : IContainer.M (C F)... | case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
i : I
x y : IContainer.M (C F)... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | . apply hβ | case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
i : I
x y : IContainer.M (C F)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | clear hβ | case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
i : I
x y : IContainer.M (C F)... | case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
i : I
x y : IContainer.M (C F)... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | intro i x y hβ | case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
i : I
x y : IContainer.M (C F)... | case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβ : I
xβ yβ : IContainer.M (C... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | simp only [precongr, map_quot] | case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβ : I
xβ yβ : IContainer.M (C... | case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβ : I
xβ yβ : IContainer.M (C... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | have hβ := hβ i _ _ hβ | case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβ : I
xβ yβ : IContainer.M (C... | case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβ : I
xβ yβ : IContainer.M (C... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | simp only [destruct, destruct.f] at hβ | case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβ : I
xβ yβ : IContainer.M (C... | case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβ : I
xβ yβ : IContainer.M (C... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | generalize IContainer.M.destruct x = x at * | case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβ : I
xβ yβ : IContainer.M (C... | case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβ : I
xβΒΉ yβ : IContainer.M (... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | generalize IContainer.M.destruct y = y at * | case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβ : I
xβΒΉ yβ : IContainer.M (... | case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβ : I
xβΒΉ yβΒΉ : IContainer.M ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | cases x with | mk nx kx =>
cases y with | mk ny ky =>
let f i : Quot (r i) β Quot (r' i) :=
by
apply Quot.lift (Quot.lift (Quot.mk (r' _)) _) _
. intro a b hβ
apply Quot.sound
simp only
rw [Quot.sound hβ]
apply hβ
. intro x; apply Quot.inductionOn (motive := _) x; clear x
int... | case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβ : I
xβΒΉ yβΒΉ : IContainer.M ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | cases y with | mk ny ky =>
let f i : Quot (r i) β Quot (r' i) :=
by
apply Quot.lift (Quot.lift (Quot.mk (r' _)) _) _
. intro a b hβ
apply Quot.sound
simp only
rw [Quot.sound hβ]
apply hβ
. intro x; apply Quot.inductionOn (motive := _) x; clear x
intro x y; apply Quot.inductio... | case a.a.mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβ : I
xβ yβΒΉ : IContainer.... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a.mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | let f i : Quot (r i) β Quot (r' i) :=
by
apply Quot.lift (Quot.lift (Quot.mk (r' _)) _) _
. intro a b hβ
apply Quot.sound
simp only
rw [Quot.sound hβ]
apply hβ
. intro x; apply Quot.inductionOn (motive := _) x; clear x
intro x y; apply Quot.inductionOn (motive := _) y; clear ... | case a.a.mk.mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβ : I
xβ yβ : IContaine... | case a.a.mk.mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβ : I
xβ yβ : IContaine... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a.mk.mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | have : β i, f i β Quot.mk (r _) β Quot.mk (congr F _) = Quot.mk (r' _) := by intro i; rfl | case a.a.mk.mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβ : I
xβ yβ : IContaine... | case a.a.mk.mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβ : I
xβ yβ : IContaine... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a.mk.mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | conv =>
congr
. rhs
lhs
intro i
rw [βthis]
rfl
. rhs
lhs
intro i
rw [βthis] | case a.a.mk.mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβ : I
xβ yβ : IContaine... | case a.a.mk.mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβ : I
xβ yβ : IContaine... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a.mk.mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | rw [IContainer.Map_spec, IContainer.Map_spec, IContainer.Map_spec, IContainer.Map_spec] | case a.a.mk.mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβ : I
xβ yβ : IContaine... | case a.a.mk.mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβ : I
xβ yβ : IContaine... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a.mk.mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | rw [inst.abs_imap, inst.abs_imap, inst.abs_imap, inst.abs_imap, inst.abs_imap, inst.abs_imap, hβ] | case a.a.mk.mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβ : I
xβ yβ : IContaine... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a.mk.mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | apply Quot.lift (Quot.lift (Quot.mk (r' _)) _) _ | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβ yβ : IContainer.M (C F) iβΒΉ
... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβ yβ : IContainer.M (C F) iβΒΉ
... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.m... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | . intro a b hβ
apply Quot.sound
simp only
rw [Quot.sound hβ]
apply hβ | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβ yβ : IContainer.M (C F) iβΒΉ
... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβ yβ : IContainer.M (C F) iβΒΉ
... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.m... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | . intro x; apply Quot.inductionOn (motive := _) x; clear x
intro x y; apply Quot.inductionOn (motive := _) y; clear y
intro y h
apply Quot.sound
apply h | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβ yβ : IContainer.M (C F) iβΒΉ
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.m... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | intro a b hβ | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβ yβ : IContainer.M (C F) iβΒΉ
... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβ yβ : IContainer.M (C F) iβΒΉ
... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.m... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | apply Quot.sound | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβ yβ : IContainer.M (C F) iβΒΉ
... | case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβ yβ : IContainer.M (C ... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.m... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | simp only | case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβ yβ : IContainer.M (C ... | case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβ yβ : IContainer.M (C ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i =>... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | rw [Quot.sound hβ] | case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβ yβ : IContainer.M (C ... | case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβ yβ : IContainer.M (C ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i =>... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | apply hβ | case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβ yβ : IContainer.M (C ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i =>... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | intro x | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβ yβ : IContainer.M (C F) iβΒΉ
... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβΒΉ yβ : IContainer.M (C F) iβΒΉ... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.m... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | apply Quot.inductionOn (motive := _) x | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβΒΉ yβ : IContainer.M (C F) iβΒΉ... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβΒΉ yβ : IContainer.M (C F) iβΒΉ... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.m... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | clear x | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβΒΉ yβ : IContainer.M (C F) iβΒΉ... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβ yβ : IContainer.M (C F) iβΒΉ
... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.m... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | intro x y | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβ yβ : IContainer.M (C F) iβΒΉ
... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβΒΉ yβΒΉ : IContainer.M (C F) iβ... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.m... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | apply Quot.inductionOn (motive := _) y | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβΒΉ yβΒΉ : IContainer.M (C F) iβ... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβΒΉ yβΒΉ : IContainer.M (C F) iβ... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.m... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | clear y | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβΒΉ yβΒΉ : IContainer.M (C F) iβ... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβΒΉ yβ : IContainer.M (C F) iβΒΉ... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.m... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | intro y h | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβΒΉ yβ : IContainer.M (C F) iβΒΉ... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβΒΉ yβΒΉ : IContainer.M (C F) iβ... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.m... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | apply Quot.sound | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβΒΉ yβΒΉ : IContainer.M (C F) iβ... | case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβΒΉ yβΒΉ : IContainer.M (... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.m... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | apply h | case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβΒΉ yβΒΉ : IContainer.M (... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i =>... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | intro i | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβ : I
xβ yβ : IContainer.M (C F) iβ
r'... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβ yβ : IContainer.M (C F) iβΒΉ
... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.m... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | rfl | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
iβΒΉ : I
xβ yβ : IContainer.M (C F) iβΒΉ
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.m... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | apply hβ | case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
i : I
x y : IContainer.M (C F)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | intro i x y hβ | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
β’ β {i : I} (x y : M F i), r i x y β x = y | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
i : I
x y : M F i
hβ : r i x y
β’ x = y | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
β’ β {i : I} (x y : M F i), r i x y β x = y
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | apply bisim_lemma (Ξ» i x y => x = y β¨ r i x y) | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
i : I
x y : M F i
hβ : r i x y
β’ x = y | case hβ
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
i : I
x y : M F i
hβ : r i x y
β’ β (i : I) (x : M F i), x = x β¨ r i x x
case hβ
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r ... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
i : I
x y : M F i
hβ : r i x y
β’ x = y
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | . intro _ _
left
rfl | case hβ
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
i : I
x y : M F i
hβ : r i x y
β’ β (i : I) (x : M F i), x = x β¨ r i x x
case hβ
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r ... | case hβ
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
i : I
x y : M F i
hβ : r i x y
β’ β (i : I) (x y : M F i),
x = y β¨ r i x y β
IFunctor.imap (fun i => Quot.mk fun x y => x = y β¨ r i ... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
i : I
x y : M F i
hβ : r i x y
β’ β (i : I) (x : M F i), x = x β¨ r i x x
case hβ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | . intro i x y hβ
cases hβ
case inl hβ =>
rw [hβ]
case inr hβ =>
have β¨z, hββ© := hβ _ _ _ hβ
clear hβ
rw [βhβ.1, βhβ.2]
clear hβ
rw [βimap_spec, βimap_spec]
conv =>
congr <;> rw [βabs_repr z]
rw [βabs_imap]
rw [βabs_imap]
cases repr z with | mk nz kz =>
simp only [... | case hβ
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
i : I
x y : M F i
hβ : r i x y
β’ β (i : I) (x y : M F i),
x = y β¨ r i x y β
IFunctor.imap (fun i => Quot.mk fun x y => x = y β¨ r i ... | case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
i : I
x y : M F i
hβ : r i x y
β’ x = y β¨ r i x y | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
i : I
x y : M F i
hβ : r i x y
β’ β (i : I) (x y : M F i),
x = y β¨ r i x y β
... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | . right; assumption | case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
i : I
x y : M F i
hβ : r i x y
β’ x = y β¨ r i x y | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
i : I
x y : M F i
hβ : r i x y
β’ x = y β¨ r i x y
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | intro _ _ | case hβ
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
i : I
x y : M F i
hβ : r i x y
β’ β (i : I) (x : M F i), x = x β¨ r i x x | case hβ
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
i : I
x y : M F i
hβ : r i x y
iβ : I
xβ : M F iβ
β’ xβ = xβ β¨ r iβ xβ xβ | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
i : I
x y : M F i
hβ : r i x y
β’ β (i : I) (x : M F i), x = x β¨ r i x x
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | left | case hβ
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
i : I
x y : M F i
hβ : r i x y
iβ : I
xβ : M F iβ
β’ xβ = xβ β¨ r iβ xβ xβ | case hβ.h
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
i : I
x y : M F i
hβ : r i x y
iβ : I
xβ : M F iβ
β’ xβ = xβ | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
i : I
x y : M F i
hβ : r i x y
iβ : I
xβ : M F iβ
β’ xβ = xβ β¨ r iβ xβ xβ
TACTIC:... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | rfl | case hβ.h
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
i : I
x y : M F i
hβ : r i x y
iβ : I
xβ : M F iβ
β’ xβ = xβ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.h
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
i : I
x y : M F i
hβ : r i x y
iβ : I
xβ : M F iβ
β’ xβ = xβ
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | intro i x y hβ | case hβ
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
i : I
x y : M F i
hβ : r i x y
β’ β (i : I) (x y : M F i),
x = y β¨ r i x y β
IFunctor.imap (fun i => Quot.mk fun x y => x = y β¨ r i ... | case hβ
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
hβ : x = y β¨ r i x y
β’ IFunctor.imap (fun i => Quot.mk fun x y => x = y β¨ r i x y) (d... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
i : I
x y : M F i
hβ : r i x y
β’ β (i : I) (x y : M F i),
x = y β¨ r i x y β
... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | cases hβ | case hβ
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
hβ : x = y β¨ r i x y
β’ IFunctor.imap (fun i => Quot.mk fun x y => x = y β¨ r i x y) (d... | case hβ.inl
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
hβ : x = y
β’ IFunctor.imap (fun i => Quot.mk fun x y => x = y β¨ r i x y) (destruc... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
hβ : x = y β¨ r i x y
β’ I... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | case inl hβ =>
rw [hβ] | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
hβ : x = y
β’ IFunctor.imap (fun i => Quot.mk fun x y => x = y β¨ r i x y) (destruct x) =
I... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
hβ : x = y
β’ IFunctor.imap (fun ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | case inr hβ =>
have β¨z, hββ© := hβ _ _ _ hβ
clear hβ
rw [βhβ.1, βhβ.2]
clear hβ
rw [βimap_spec, βimap_spec]
conv =>
congr <;> rw [βabs_repr z]
rw [βabs_imap]
rw [βabs_imap]
cases repr z with | mk nz kz =>
simp only [IContainer.Map, Function.comp]
apply congrArg abs
rw [Sigma.mk.inj_iff]
sim... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
hβ : r i x y
β’ IFunctor.imap (fun i => Quot.mk fun x y => x = y β¨ r i x y) (destruct x) =
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
hβ : r i x y
β’ IFunctor.imap (fu... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | rw [hβ] | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
hβ : x = y
β’ IFunctor.imap (fun i => Quot.mk fun x y => x = y β¨ r i x y) (destruct x) =
I... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
hβ : x = y
β’ IFunctor.imap (fun ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | have β¨z, hββ© := hβ _ _ _ hβ | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
hβ : r i x y
β’ IFunctor.imap (fun i => Quot.mk fun x y => x = y β¨ r i x y) (destruct x) =
... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
hβ : r i x y
z : F (fun i => { p // r i p.fst p.snd }) i
hβ : IFunctor.imap (fun x x_1 => (βx... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
hβ : r i x y
β’ IFunctor.imap (fu... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | clear hβ | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
hβ : r i x y
z : F (fun i => { p // r i p.fst p.snd }) i
hβ : IFunctor.imap (fun x x_1 => (βx... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
hβ : IFunctor.imap (fun x x_1 => (βx_1).fst) z = ... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
hβ : r i x y
z : F (fun i => { p... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | rw [βhβ.1, βhβ.2] | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
hβ : IFunctor.imap (fun x x_1 => (βx_1).fst) z = ... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
hβ : IFunctor.imap (fun x x_1 => (βx_1).fst) z = ... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | clear hβ | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
hβ : IFunctor.imap (fun x x_1 => (βx_1).fst) z = ... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
β’ IFunctor.imap (fun i => Quot.mk fun x y => x = ... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | rw [βimap_spec, βimap_spec] | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
β’ IFunctor.imap (fun i => Quot.mk fun x y => x = ... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
β’ IFunctor.imap (fun i => (Quot.mk fun x y => x =... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | conv =>
congr <;> rw [βabs_repr z] | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
β’ IFunctor.imap (fun i => (Quot.mk fun x y => x =... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
β’ IFunctor.imap (fun i => (Quot.mk fun x y => x =... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | rw [βabs_imap] | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
β’ IFunctor.imap (fun i => (Quot.mk fun x y => x =... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
β’ abs (IContainer.Map (fun i => (Quot.mk fun x y ... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | rw [βabs_imap] | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
β’ abs (IContainer.Map (fun i => (Quot.mk fun x y ... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
β’ abs (IContainer.Map (fun i => (Quot.mk fun x y ... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | cases repr z with | mk nz kz =>
simp only [IContainer.Map, Function.comp]
apply congrArg abs
rw [Sigma.mk.inj_iff]
simp only [true_and, heq_eq_eq]
funext a
apply Quot.sound
right
apply (kz a).2 | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
β’ abs (IContainer.Map (fun i => (Quot.mk fun x y ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | simp only [IContainer.Map, Function.comp] | case mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
nz : IContainer.A (C F) i
kz : (y : ICont... | case mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
nz : IContainer.A (C F) i
kz : (y : ICont... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | apply congrArg abs | case mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
nz : IContainer.A (C F) i
kz : (y : ICont... | case mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
nz : IContainer.A (C F) i
kz : (y : ICont... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | rw [Sigma.mk.inj_iff] | case mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
nz : IContainer.A (C F) i
kz : (y : ICont... | case mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
nz : IContainer.A (C F) i
kz : (y : ICont... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | simp only [true_and, heq_eq_eq] | case mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
nz : IContainer.A (C F) i
kz : (y : ICont... | case mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
nz : IContainer.A (C F) i
kz : (y : ICont... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | funext a | case mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
nz : IContainer.A (C F) i
kz : (y : ICont... | case mk.h
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
nz : IContainer.A (C F) i
kz : (y : ICo... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | apply Quot.sound | case mk.h
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
nz : IContainer.A (C F) i
kz : (y : ICo... | case mk.h.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
nz : IContainer.A (C F) i
kz : (y : I... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk.h
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p //... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | right | case mk.h.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
nz : IContainer.A (C F) i
kz : (y : I... | case mk.h.a.h
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
nz : IContainer.A (C F) i
kz : (y :... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk.h.a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | apply (kz a).2 | case mk.h.a.h
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { p // r i p.fst p.snd }) i
nz : IContainer.A (C F) i
kz : (y :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mk.h.a.h
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
iβ : I
xβ yβ : M F iβ
hβ : r iβ xβ yβ
i : I
x y : M F i
z : F (fun i => { ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | right | case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
i : I
x y : M F i
hβ : r i x y
β’ x = y β¨ r i x y | case a.h
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
i : I
x y : M F i
hβ : r i x y
β’ r i x y | Please generate a tactic in lean4 to solve the state.
STATE:
case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
i : I
x y : M F i
hβ : r i x y
β’ x = y β¨ r i x y
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim | [185, 1] | [216, 22] | assumption | case a.h
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
i : I
x y : M F i
hβ : r i x y
β’ r i x y | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x y : M F i), r i x y β liftr F r i (destruct x) (destruct y)
i : I
x y : M F i
hβ : r i x y
β’ r i x y
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.congr.coinduction | [56, 1] | [67, 13] | intro hβ x y hβ | Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
β’ (β (x y : M (C F)), p x y β β(precongr F) p x y) β β (x y : M (C F)), p x y β congr F x y | Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
hβ : β (x y : M (C F)), p x y β β(precongr F) p x y
x y : M (C F)
hβ : p x y
β’ congr F x y | Please generate a tactic in lean4 to solve the state.
STATE:
Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
β’ (β (x y : M (C F)), p x y β β(precongr F) p x y) β β (x y : M (C F)), p x y β congr F x y
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.congr.coinduction | [56, 1] | [67, 13] | simp only [congr, pcongr] | Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
hβ : β (x y : M (C F)), p x y β β(precongr F) p x y
x y : M (C F)
hβ : p x y
β’ congr F x y | Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
hβ : β (x y : M (C F)), p x y β β(precongr F) p x y
x y : M (C F)
hβ : p x y
β’ β(pgfp (precongr F)) β₯ x y | Please generate a tactic in lean4 to solve the state.
STATE:
Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
hβ : β (x y : M (C F)), p x y β β(precongr F) p x y
x y : M (C F)
hβ : p x y
β’ congr F x y
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.congr.coinduction | [56, 1] | [67, 13] | have := (pgfp.coinduction (precongr F) p).2 | Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
hβ : β (x y : M (C F)), p x y β β(precongr F) p x y
x y : M (C F)
hβ : p x y
β’ β(pgfp (precongr F)) β₯ x y | Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
hβ : β (x y : M (C F)), p x y β β(precongr F) p x y
x y : M (C F)
hβ : p x y
this : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F)) β₯
β’ β(pgfp (precongr F)) β₯ x y | Please generate a tactic in lean4 to solve the state.
STATE:
Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
hβ : β (x y : M (C F)), p x y β β(precongr F) p x y
x y : M (C F)
hβ : p x y
β’ β(pgfp (precongr F)) β₯ x y
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.congr.coinduction | [56, 1] | [67, 13] | apply this | Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
hβ : β (x y : M (C F)), p x y β β(precongr F) p x y
x y : M (C F)
hβ : p x y
this : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F)) β₯
β’ β(pgfp (precongr F)) β₯ x y | case a
Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
hβ : β (x y : M (C F)), p x y β β(precongr F) p x y
x y : M (C F)
hβ : p x y
this : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F)) β₯
β’ p β€ β(precongr F) (p β β(pgfp (precongr F)) p)
c... | Please generate a tactic in lean4 to solve the state.
STATE:
Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
hβ : β (x y : M (C F)), p x y β β(precongr F) p x y
x y : M (C F)
hβ : p x y
this : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F))... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.congr.coinduction | [56, 1] | [67, 13] | have : p β€ p β pgfp (precongr F) p := by
simp | case a
Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
hβ : β (x y : M (C F)), p x y β β(precongr F) p x y
x y : M (C F)
hβ : p x y
this : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F)) β₯
β’ p β€ β(precongr F) (p β β(pgfp (precongr F)) p)
c... | case a
Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
hβ : β (x y : M (C F)), p x y β β(precongr F) p x y
x y : M (C F)
hβ : p x y
thisβ : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F)) β₯
this : p β€ p β β(pgfp (precongr F)) p
β’ p β€ β(prec... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
hβ : β (x y : M (C F)), p x y β β(precongr F) p x y
x y : M (C F)
hβ : p x y
this : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (preco... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.congr.coinduction | [56, 1] | [67, 13] | have := (precongr F).2 this | case a
Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
hβ : β (x y : M (C F)), p x y β β(precongr F) p x y
x y : M (C F)
hβ : p x y
thisβ : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F)) β₯
this : p β€ p β β(pgfp (precongr F)) p
β’ p β€ β(prec... | case a
Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
hβ : β (x y : M (C F)), p x y β β(precongr F) p x y
x y : M (C F)
hβ : p x y
thisβΒΉ : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F)) β₯
thisβ : p β€ p β β(pgfp (precongr F)) p
this : β(p... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
hβ : β (x y : M (C F)), p x y β β(precongr F) p x y
x y : M (C F)
hβ : p x y
thisβ : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (prec... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.congr.coinduction | [56, 1] | [67, 13] | apply le_trans _ this | case a
Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
hβ : β (x y : M (C F)), p x y β β(precongr F) p x y
x y : M (C F)
hβ : p x y
thisβΒΉ : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F)) β₯
thisβ : p β€ p β β(pgfp (precongr F)) p
this : β(p... | Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
hβ : β (x y : M (C F)), p x y β β(precongr F) p x y
x y : M (C F)
hβ : p x y
thisβΒΉ : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F)) β₯
thisβ : p β€ p β β(pgfp (precongr F)) p
this : β(precongr... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
hβ : β (x y : M (C F)), p x y β β(precongr F) p x y
x y : M (C F)
hβ : p x y
thisβΒΉ : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (pre... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.congr.coinduction | [56, 1] | [67, 13] | apply hβ | Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
hβ : β (x y : M (C F)), p x y β β(precongr F) p x y
x y : M (C F)
hβ : p x y
thisβΒΉ : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F)) β₯
thisβ : p β€ p β β(pgfp (precongr F)) p
this : β(precongr... | case a
Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
hβ : β (x y : M (C F)), p x y β β(precongr F) p x y
x y : M (C F)
hβ : p x y
this : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F)) β₯
β’ p x y | Please generate a tactic in lean4 to solve the state.
STATE:
Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
hβ : β (x y : M (C F)), p x y β β(precongr F) p x y
x y : M (C F)
hβ : p x y
thisβΒΉ : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.congr.coinduction | [56, 1] | [67, 13] | assumption | case a
Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
hβ : β (x y : M (C F)), p x y β β(precongr F) p x y
x y : M (C F)
hβ : p x y
this : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F)) β₯
β’ p x y | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
hβ : β (x y : M (C F)), p x y β β(precongr F) p x y
x y : M (C F)
hβ : p x y
this : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (preco... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.congr.coinduction | [56, 1] | [67, 13] | simp | Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
hβ : β (x y : M (C F)), p x y β β(precongr F) p x y
x y : M (C F)
hβ : p x y
this : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F)) β₯
β’ p β€ p β β(pgfp (precongr F)) p | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Fβ : Type uβ β Type uβ
instβ : QPF Fβ
F : Type uβ β Type uβ
inst : QPF F
p : M (C F) β M (C F) β Prop
hβ : β (x y : M (C F)), p x y β β(precongr F) p x y
x y : M (C F)
hβ : p x y
this : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F))... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.destruct_corec | [98, 1] | [105, 8] | simp only [destruct, corec, destruct.f, Container.M.destruct_corec, inst.abs_map, inst.abs_repr] | F : Type uβ β Type uβ
inst : QPF F
Ξ± : Type uβ
f : Ξ± β F Ξ±
xβ : Ξ±
β’ destruct (corec f xβ) = (fun x => corec f x) <$> f xβ | F : Type uβ β Type uβ
inst : QPF F
Ξ± : Type uβ
f : Ξ± β F Ξ±
xβ : Ξ±
β’ (fun x => Quot.mk (congr F) x) <$> (Container.M.corec fun x => repr (f x)) <$> f xβ =
(fun x => Quot.mk (congr F) (Container.M.corec (fun x => repr (f x)) x)) <$> f xβ | Please generate a tactic in lean4 to solve the state.
STATE:
F : Type uβ β Type uβ
inst : QPF F
Ξ± : Type uβ
f : Ξ± β F Ξ±
xβ : Ξ±
β’ destruct (corec f xβ) = (fun x => corec f x) <$> f xβ
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.destruct_corec | [98, 1] | [105, 8] | rw [βinst.abs_repr (f xβ)] | F : Type uβ β Type uβ
inst : QPF F
Ξ± : Type uβ
f : Ξ± β F Ξ±
xβ : Ξ±
β’ (fun x => Quot.mk (congr F) x) <$> (Container.M.corec fun x => repr (f x)) <$> f xβ =
(fun x => Quot.mk (congr F) (Container.M.corec (fun x => repr (f x)) x)) <$> f xβ | F : Type uβ β Type uβ
inst : QPF F
Ξ± : Type uβ
f : Ξ± β F Ξ±
xβ : Ξ±
β’ (fun x => Quot.mk (congr F) x) <$> (Container.M.corec fun x => repr (f x)) <$> abs (repr (f xβ)) =
(fun x => Quot.mk (congr F) (Container.M.corec (fun x => repr (f x)) x)) <$> abs (repr (f xβ)) | Please generate a tactic in lean4 to solve the state.
STATE:
F : Type uβ β Type uβ
inst : QPF F
Ξ± : Type uβ
f : Ξ± β F Ξ±
xβ : Ξ±
β’ (fun x => Quot.mk (congr F) x) <$> (Container.M.corec fun x => repr (f x)) <$> f xβ =
(fun x => Quot.mk (congr F) (Container.M.corec (fun x => repr (f x)) x)) <$> f xβ
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.destruct_corec | [98, 1] | [105, 8] | cases repr (f xβ) with
| mk n k =>
simp only [βinst.abs_map, Container.Map]
rfl | F : Type uβ β Type uβ
inst : QPF F
Ξ± : Type uβ
f : Ξ± β F Ξ±
xβ : Ξ±
β’ (fun x => Quot.mk (congr F) x) <$> (Container.M.corec fun x => repr (f x)) <$> abs (repr (f xβ)) =
(fun x => Quot.mk (congr F) (Container.M.corec (fun x => repr (f x)) x)) <$> abs (repr (f xβ)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
F : Type uβ β Type uβ
inst : QPF F
Ξ± : Type uβ
f : Ξ± β F Ξ±
xβ : Ξ±
β’ (fun x => Quot.mk (congr F) x) <$> (Container.M.corec fun x => repr (f x)) <$> abs (repr (f xβ)) =
(fun x => Quot.mk (congr F) (Container.M.corec (fun x => repr (f x)) x)) <$> abs (repr (... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.destruct_corec | [98, 1] | [105, 8] | simp only [βinst.abs_map, Container.Map] | case mk
F : Type uβ β Type uβ
inst : QPF F
Ξ± : Type uβ
f : Ξ± β F Ξ±
xβ : Ξ±
n : (C F).A
k : Container.B (C F) n β Ξ±
β’ (fun x => Quot.mk (congr F) x) <$> (Container.M.corec fun x => repr (f x)) <$> abs { fst := n, snd := k } =
(fun x => Quot.mk (congr F) (Container.M.corec (fun x => repr (f x)) x)) <$> abs { fst := n,... | case mk
F : Type uβ β Type uβ
inst : QPF F
Ξ± : Type uβ
f : Ξ± β F Ξ±
xβ : Ξ±
n : (C F).A
k : Container.B (C F) n β Ξ±
β’ abs { fst := n, snd := (fun x => Quot.mk (congr F) x) β (Container.M.corec fun x => repr (f x)) β k } =
abs { fst := n, snd := (fun x => Quot.mk (congr F) (Container.M.corec (fun x => repr (f x)) x)) ... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
F : Type uβ β Type uβ
inst : QPF F
Ξ± : Type uβ
f : Ξ± β F Ξ±
xβ : Ξ±
n : (C F).A
k : Container.B (C F) n β Ξ±
β’ (fun x => Quot.mk (congr F) x) <$> (Container.M.corec fun x => repr (f x)) <$> abs { fst := n, snd := k } =
(fun x => Quot.mk (congr F) (Co... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.destruct_corec | [98, 1] | [105, 8] | rfl | case mk
F : Type uβ β Type uβ
inst : QPF F
Ξ± : Type uβ
f : Ξ± β F Ξ±
xβ : Ξ±
n : (C F).A
k : Container.B (C F) n β Ξ±
β’ abs { fst := n, snd := (fun x => Quot.mk (congr F) x) β (Container.M.corec fun x => repr (f x)) β k } =
abs { fst := n, snd := (fun x => Quot.mk (congr F) (Container.M.corec (fun x => repr (f x)) x)) ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
F : Type uβ β Type uβ
inst : QPF F
Ξ± : Type uβ
f : Ξ± β F Ξ±
xβ : Ξ±
n : (C F).A
k : Container.B (C F) n β Ξ±
β’ abs { fst := n, snd := (fun x => Quot.mk (congr F) x) β (Container.M.corec fun x => repr (f x)) β k } =
abs { fst := n, snd := (fun x => Qu... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.map_comp | [119, 1] | [126, 6] | conv =>
congr
<;> rw [βinst.abs_repr x] | F : Type uβ β Type uβ
inst : QPF F
Ξ± Ξ² Ξ³ : Type uβ
f : Ξ² β Ξ³
g : Ξ± β Ξ²
x : F Ξ±
β’ (f β g) <$> x = f <$> g <$> x | F : Type uβ β Type uβ
inst : QPF F
Ξ± Ξ² Ξ³ : Type uβ
f : Ξ² β Ξ³
g : Ξ± β Ξ²
x : F Ξ±
β’ (f β g) <$> abs (repr x) = f <$> g <$> abs (repr x) | Please generate a tactic in lean4 to solve the state.
STATE:
F : Type uβ β Type uβ
inst : QPF F
Ξ± Ξ² Ξ³ : Type uβ
f : Ξ² β Ξ³
g : Ξ± β Ξ²
x : F Ξ±
β’ (f β g) <$> x = f <$> g <$> x
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.map_comp | [119, 1] | [126, 6] | cases repr x | F : Type uβ β Type uβ
inst : QPF F
Ξ± Ξ² Ξ³ : Type uβ
f : Ξ² β Ξ³
g : Ξ± β Ξ²
x : F Ξ±
β’ (f β g) <$> abs (repr x) = f <$> g <$> abs (repr x) | case mk
F : Type uβ β Type uβ
inst : QPF F
Ξ± Ξ² Ξ³ : Type uβ
f : Ξ² β Ξ³
g : Ξ± β Ξ²
x : F Ξ±
fstβ : (C F).A
sndβ : Container.B (C F) fstβ β Ξ±
β’ (f β g) <$> abs { fst := fstβ, snd := sndβ } = f <$> g <$> abs { fst := fstβ, snd := sndβ } | Please generate a tactic in lean4 to solve the state.
STATE:
F : Type uβ β Type uβ
inst : QPF F
Ξ± Ξ² Ξ³ : Type uβ
f : Ξ² β Ξ³
g : Ξ± β Ξ²
x : F Ξ±
β’ (f β g) <$> abs (repr x) = f <$> g <$> abs (repr x)
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.map_comp | [119, 1] | [126, 6] | simp [βinst.abs_map, Container.Map] | case mk
F : Type uβ β Type uβ
inst : QPF F
Ξ± Ξ² Ξ³ : Type uβ
f : Ξ² β Ξ³
g : Ξ± β Ξ²
x : F Ξ±
fstβ : (C F).A
sndβ : Container.B (C F) fstβ β Ξ±
β’ (f β g) <$> abs { fst := fstβ, snd := sndβ } = f <$> g <$> abs { fst := fstβ, snd := sndβ } | case mk
F : Type uβ β Type uβ
inst : QPF F
Ξ± Ξ² Ξ³ : Type uβ
f : Ξ² β Ξ³
g : Ξ± β Ξ²
x : F Ξ±
fstβ : (C F).A
sndβ : Container.B (C F) fstβ β Ξ±
β’ abs { fst := fstβ, snd := (f β g) β sndβ } = abs { fst := fstβ, snd := f β g β sndβ } | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
F : Type uβ β Type uβ
inst : QPF F
Ξ± Ξ² Ξ³ : Type uβ
f : Ξ² β Ξ³
g : Ξ± β Ξ²
x : F Ξ±
fstβ : (C F).A
sndβ : Container.B (C F) fstβ β Ξ±
β’ (f β g) <$> abs { fst := fstβ, snd := sndβ } = f <$> g <$> abs { fst := fstβ, snd := sndβ }
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.map_comp | [119, 1] | [126, 6] | rfl | case mk
F : Type uβ β Type uβ
inst : QPF F
Ξ± Ξ² Ξ³ : Type uβ
f : Ξ² β Ξ³
g : Ξ± β Ξ²
x : F Ξ±
fstβ : (C F).A
sndβ : Container.B (C F) fstβ β Ξ±
β’ abs { fst := fstβ, snd := (f β g) β sndβ } = abs { fst := fstβ, snd := f β g β sndβ } | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
F : Type uβ β Type uβ
inst : QPF F
Ξ± Ξ² Ξ³ : Type uβ
f : Ξ² β Ξ³
g : Ξ± β Ξ²
x : F Ξ±
fstβ : (C F).A
sndβ : Container.B (C F) fstβ β Ξ±
β’ abs { fst := fstβ, snd := (f β g) β sndβ } = abs { fst := fstβ, snd := f β g β sndβ }
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | Container.Map_spec | [129, 1] | [133, 6] | cases x | F : Type uβ β Type uβ
inst : QPF F
Ξ± Ξ² Ξ³ : Type uβ
f : Ξ² β Ξ³
g : Ξ± β Ξ²
x : Obj (QPF.C F) Ξ±
β’ Map (f β g) x = Map f (Map g x) | case mk
F : Type uβ β Type uβ
inst : QPF F
Ξ± Ξ² Ξ³ : Type uβ
f : Ξ² β Ξ³
g : Ξ± β Ξ²
fstβ : (QPF.C F).A
sndβ : B (QPF.C F) fstβ β Ξ±
β’ Map (f β g) { fst := fstβ, snd := sndβ } = Map f (Map g { fst := fstβ, snd := sndβ }) | Please generate a tactic in lean4 to solve the state.
STATE:
F : Type uβ β Type uβ
inst : QPF F
Ξ± Ξ² Ξ³ : Type uβ
f : Ξ² β Ξ³
g : Ξ± β Ξ²
x : Obj (QPF.C F) Ξ±
β’ Map (f β g) x = Map f (Map g x)
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | Container.Map_spec | [129, 1] | [133, 6] | simp [Map] | case mk
F : Type uβ β Type uβ
inst : QPF F
Ξ± Ξ² Ξ³ : Type uβ
f : Ξ² β Ξ³
g : Ξ± β Ξ²
fstβ : (QPF.C F).A
sndβ : B (QPF.C F) fstβ β Ξ±
β’ Map (f β g) { fst := fstβ, snd := sndβ } = Map f (Map g { fst := fstβ, snd := sndβ }) | case mk
F : Type uβ β Type uβ
inst : QPF F
Ξ± Ξ² Ξ³ : Type uβ
f : Ξ² β Ξ³
g : Ξ± β Ξ²
fstβ : (QPF.C F).A
sndβ : B (QPF.C F) fstβ β Ξ±
β’ (f β g) β sndβ = f β g β sndβ | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
F : Type uβ β Type uβ
inst : QPF F
Ξ± Ξ² Ξ³ : Type uβ
f : Ξ² β Ξ³
g : Ξ± β Ξ²
fstβ : (QPF.C F).A
sndβ : B (QPF.C F) fstβ β Ξ±
β’ Map (f β g) { fst := fstβ, snd := sndβ } = Map f (Map g { fst := fstβ, snd := sndβ })
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | Container.Map_spec | [129, 1] | [133, 6] | rfl | case mk
F : Type uβ β Type uβ
inst : QPF F
Ξ± Ξ² Ξ³ : Type uβ
f : Ξ² β Ξ³
g : Ξ± β Ξ²
fstβ : (QPF.C F).A
sndβ : B (QPF.C F) fstβ β Ξ±
β’ (f β g) β sndβ = f β g β sndβ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
F : Type uβ β Type uβ
inst : QPF F
Ξ± Ξ² Ξ³ : Type uβ
f : Ξ² β Ξ³
g : Ξ± β Ξ²
fstβ : (QPF.C F).A
sndβ : B (QPF.C F) fstβ β Ξ±
β’ (f β g) β sndβ = f β g β sndβ
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.bisim_lemma | [135, 1] | [187, 13] | intro x | F : Type uβ β Type uβ
inst : QPF F
r : M F β M F β Prop
hβ : β (x : M F), r x x
hβ : β (x y : M F), r x y β Quot.mk r <$> destruct x = Quot.mk r <$> destruct y
β’ β (x y : M F), r x y β x = y | F : Type uβ β Type uβ
inst : QPF F
r : M F β M F β Prop
hβ : β (x : M F), r x x
hβ : β (x y : M F), r x y β Quot.mk r <$> destruct x = Quot.mk r <$> destruct y
x : M F
β’ β (y : M F), r x y β x = y | Please generate a tactic in lean4 to solve the state.
STATE:
F : Type uβ β Type uβ
inst : QPF F
r : M F β M F β Prop
hβ : β (x : M F), r x x
hβ : β (x y : M F), r x y β Quot.mk r <$> destruct x = Quot.mk r <$> destruct y
β’ β (x y : M F), r x y β x = y
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.bisim_lemma | [135, 1] | [187, 13] | apply Quot.inductionOn (motive := _) x | F : Type uβ β Type uβ
inst : QPF F
r : M F β M F β Prop
hβ : β (x : M F), r x x
hβ : β (x y : M F), r x y β Quot.mk r <$> destruct x = Quot.mk r <$> destruct y
x : M F
β’ β (y : M F), r x y β x = y | F : Type uβ β Type uβ
inst : QPF F
r : M F β M F β Prop
hβ : β (x : M F), r x x
hβ : β (x y : M F), r x y β Quot.mk r <$> destruct x = Quot.mk r <$> destruct y
x : M F
β’ β (a : Container.M (C F)) (y : M F), r (Quot.mk (congr F) a) y β Quot.mk (congr F) a = y | Please generate a tactic in lean4 to solve the state.
STATE:
F : Type uβ β Type uβ
inst : QPF F
r : M F β M F β Prop
hβ : β (x : M F), r x x
hβ : β (x y : M F), r x y β Quot.mk r <$> destruct x = Quot.mk r <$> destruct y
x : M F
β’ β (y : M F), r x y β x = y
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.bisim_lemma | [135, 1] | [187, 13] | clear x | F : Type uβ β Type uβ
inst : QPF F
r : M F β M F β Prop
hβ : β (x : M F), r x x
hβ : β (x y : M F), r x y β Quot.mk r <$> destruct x = Quot.mk r <$> destruct y
x : M F
β’ β (a : Container.M (C F)) (y : M F), r (Quot.mk (congr F) a) y β Quot.mk (congr F) a = y | F : Type uβ β Type uβ
inst : QPF F
r : M F β M F β Prop
hβ : β (x : M F), r x x
hβ : β (x y : M F), r x y β Quot.mk r <$> destruct x = Quot.mk r <$> destruct y
β’ β (a : Container.M (C F)) (y : M F), r (Quot.mk (congr F) a) y β Quot.mk (congr F) a = y | Please generate a tactic in lean4 to solve the state.
STATE:
F : Type uβ β Type uβ
inst : QPF F
r : M F β M F β Prop
hβ : β (x : M F), r x x
hβ : β (x y : M F), r x y β Quot.mk r <$> destruct x = Quot.mk r <$> destruct y
x : M F
β’ β (a : Container.M (C F)) (y : M F), r (Quot.mk (congr F) a) y β Quot.mk (congr F) a = y
... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.bisim_lemma | [135, 1] | [187, 13] | intro x y | F : Type uβ β Type uβ
inst : QPF F
r : M F β M F β Prop
hβ : β (x : M F), r x x
hβ : β (x y : M F), r x y β Quot.mk r <$> destruct x = Quot.mk r <$> destruct y
β’ β (a : Container.M (C F)) (y : M F), r (Quot.mk (congr F) a) y β Quot.mk (congr F) a = y | F : Type uβ β Type uβ
inst : QPF F
r : M F β M F β Prop
hβ : β (x : M F), r x x
hβ : β (x y : M F), r x y β Quot.mk r <$> destruct x = Quot.mk r <$> destruct y
x : Container.M (C F)
y : M F
β’ r (Quot.mk (congr F) x) y β Quot.mk (congr F) x = y | Please generate a tactic in lean4 to solve the state.
STATE:
F : Type uβ β Type uβ
inst : QPF F
r : M F β M F β Prop
hβ : β (x : M F), r x x
hβ : β (x y : M F), r x y β Quot.mk r <$> destruct x = Quot.mk r <$> destruct y
β’ β (a : Container.M (C F)) (y : M F), r (Quot.mk (congr F) a) y β Quot.mk (congr F) a = y
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.bisim_lemma | [135, 1] | [187, 13] | apply Quot.inductionOn (motive := _) y | F : Type uβ β Type uβ
inst : QPF F
r : M F β M F β Prop
hβ : β (x : M F), r x x
hβ : β (x y : M F), r x y β Quot.mk r <$> destruct x = Quot.mk r <$> destruct y
x : Container.M (C F)
y : M F
β’ r (Quot.mk (congr F) x) y β Quot.mk (congr F) x = y | F : Type uβ β Type uβ
inst : QPF F
r : M F β M F β Prop
hβ : β (x : M F), r x x
hβ : β (x y : M F), r x y β Quot.mk r <$> destruct x = Quot.mk r <$> destruct y
x : Container.M (C F)
y : M F
β’ β (a : Container.M (C F)), r (Quot.mk (congr F) x) (Quot.mk (congr F) a) β Quot.mk (congr F) x = Quot.mk (congr F) a | Please generate a tactic in lean4 to solve the state.
STATE:
F : Type uβ β Type uβ
inst : QPF F
r : M F β M F β Prop
hβ : β (x : M F), r x x
hβ : β (x y : M F), r x y β Quot.mk r <$> destruct x = Quot.mk r <$> destruct y
x : Container.M (C F)
y : M F
β’ r (Quot.mk (congr F) x) y β Quot.mk (congr F) x = y
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.bisim_lemma | [135, 1] | [187, 13] | clear y | F : Type uβ β Type uβ
inst : QPF F
r : M F β M F β Prop
hβ : β (x : M F), r x x
hβ : β (x y : M F), r x y β Quot.mk r <$> destruct x = Quot.mk r <$> destruct y
x : Container.M (C F)
y : M F
β’ β (a : Container.M (C F)), r (Quot.mk (congr F) x) (Quot.mk (congr F) a) β Quot.mk (congr F) x = Quot.mk (congr F) a | F : Type uβ β Type uβ
inst : QPF F
r : M F β M F β Prop
hβ : β (x : M F), r x x
hβ : β (x y : M F), r x y β Quot.mk r <$> destruct x = Quot.mk r <$> destruct y
x : Container.M (C F)
β’ β (a : Container.M (C F)), r (Quot.mk (congr F) x) (Quot.mk (congr F) a) β Quot.mk (congr F) x = Quot.mk (congr F) a | Please generate a tactic in lean4 to solve the state.
STATE:
F : Type uβ β Type uβ
inst : QPF F
r : M F β M F β Prop
hβ : β (x : M F), r x x
hβ : β (x y : M F), r x y β Quot.mk r <$> destruct x = Quot.mk r <$> destruct y
x : Container.M (C F)
y : M F
β’ β (a : Container.M (C F)), r (Quot.mk (congr F) x) (Quot.mk (congr ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.bisim_lemma | [135, 1] | [187, 13] | intro y hβ | F : Type uβ β Type uβ
inst : QPF F
r : M F β M F β Prop
hβ : β (x : M F), r x x
hβ : β (x y : M F), r x y β Quot.mk r <$> destruct x = Quot.mk r <$> destruct y
x : Container.M (C F)
β’ β (a : Container.M (C F)), r (Quot.mk (congr F) x) (Quot.mk (congr F) a) β Quot.mk (congr F) x = Quot.mk (congr F) a | F : Type uβ β Type uβ
inst : QPF F
r : M F β M F β Prop
hβ : β (x : M F), r x x
hβ : β (x y : M F), r x y β Quot.mk r <$> destruct x = Quot.mk r <$> destruct y
x y : Container.M (C F)
hβ : r (Quot.mk (congr F) x) (Quot.mk (congr F) y)
β’ Quot.mk (congr F) x = Quot.mk (congr F) y | Please generate a tactic in lean4 to solve the state.
STATE:
F : Type uβ β Type uβ
inst : QPF F
r : M F β M F β Prop
hβ : β (x : M F), r x x
hβ : β (x y : M F), r x y β Quot.mk r <$> destruct x = Quot.mk r <$> destruct y
x : Container.M (C F)
β’ β (a : Container.M (C F)), r (Quot.mk (congr F) x) (Quot.mk (congr F) a) β ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.bisim_lemma | [135, 1] | [187, 13] | apply Quot.sound | F : Type uβ β Type uβ
inst : QPF F
r : M F β M F β Prop
hβ : β (x : M F), r x x
hβ : β (x y : M F), r x y β Quot.mk r <$> destruct x = Quot.mk r <$> destruct y
x y : Container.M (C F)
hβ : r (Quot.mk (congr F) x) (Quot.mk (congr F) y)
β’ Quot.mk (congr F) x = Quot.mk (congr F) y | case a
F : Type uβ β Type uβ
inst : QPF F
r : M F β M F β Prop
hβ : β (x : M F), r x x
hβ : β (x y : M F), r x y β Quot.mk r <$> destruct x = Quot.mk r <$> destruct y
x y : Container.M (C F)
hβ : r (Quot.mk (congr F) x) (Quot.mk (congr F) y)
β’ congr F x y | Please generate a tactic in lean4 to solve the state.
STATE:
F : Type uβ β Type uβ
inst : QPF F
r : M F β M F β Prop
hβ : β (x : M F), r x x
hβ : β (x y : M F), r x y β Quot.mk r <$> destruct x = Quot.mk r <$> destruct y
x y : Container.M (C F)
hβ : r (Quot.mk (congr F) x) (Quot.mk (congr F) y)
β’ Quot.mk (congr F) x = ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/M.lean | QPF.M.bisim_lemma | [135, 1] | [187, 13] | let r' x y := r (Quot.mk _ x) (Quot.mk _ y) | case a
F : Type uβ β Type uβ
inst : QPF F
r : M F β M F β Prop
hβ : β (x : M F), r x x
hβ : β (x y : M F), r x y β Quot.mk r <$> destruct x = Quot.mk r <$> destruct y
x y : Container.M (C F)
hβ : r (Quot.mk (congr F) x) (Quot.mk (congr F) y)
β’ congr F x y | case a
F : Type uβ β Type uβ
inst : QPF F
r : M F β M F β Prop
hβ : β (x : M F), r x x
hβ : β (x y : M F), r x y β Quot.mk r <$> destruct x = Quot.mk r <$> destruct y
x y : Container.M (C F)
hβ : r (Quot.mk (congr F) x) (Quot.mk (congr F) y)
r' : Container.M (C F) β Container.M (C F) β Prop := fun x y => r (Quot.mk (co... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
F : Type uβ β Type uβ
inst : QPF F
r : M F β M F β Prop
hβ : β (x : M F), r x x
hβ : β (x y : M F), r x y β Quot.mk r <$> destruct x = Quot.mk r <$> destruct y
x y : Container.M (C F)
hβ : r (Quot.mk (congr F) x) (Quot.mk (congr F) y)
β’ congr F x y
TAC... |
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